Moment of inertia of a system of masses

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SUMMARY

The moment of inertia for a system consisting of two masses, 3.0 kg and 5.0 kg, connected by a rod of negligible mass measuring 0.8 m, is calculated using the equation I = I1 + I2. The correct moment of inertia is determined to be 2 kg m², derived from the center of mass position and the respective distances of the masses. The equation (m1+m2)R = m1r1 + m2r2 is crucial for finding the center of mass, where R represents the center of mass position, and r1 and r2 are the distances of the masses from this point. Understanding these calculations is essential for accurately determining the moment of inertia in similar systems.

PREREQUISITES
  • Understanding of moment of inertia calculations
  • Familiarity with the concept of center of mass
  • Basic algebra for solving equations
  • Knowledge of torque and its relation to forces
NEXT STEPS
  • Learn how to derive the center of mass for different mass distributions
  • Study the principles of torque and its impact on rotational dynamics
  • Explore advanced moment of inertia calculations for complex systems
  • Research various methods for experimentally determining the center of mass
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators and anyone interested in understanding the principles of rotational motion and moment of inertia calculations.

Pablo
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Homework Statement



The moment of inertia about an axis through the center of mass of a system consisting of two masses 3.0 and 5.0 kg connected by a rod of negligible mass 0.8m long is

Homework Equations


[/B]
I = I1 + I2

The Attempt at a Solution



I added all the moments of inertia of the system about the middle (0.4m)

I = m1R^2 + m2R^2 = (m1 + m2) * R^2 = (3 + 5) * 0.4^2 = 1.28

However, 1.28 is not the right answers. Does anyone know where I went wrong?
 
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I am no expert but my syllabus is same
I am trying for practice
(m1+m2)R=m1r1+m2r2
8(R)=3(0)+5(0.8)
8R=4
R=1/2
Mment of inertia=MR^2
=8 1/4
=2 Kg m^2
is this correct please tell me
 
Suyash Singh said:
I am no expert but my syllabus is same
I am trying for practice
(m1+m2)R=m1r1+m2r2
8(R)=3(0)+5(0.8)
8R=4
R=1/2
Mment of inertia=MR^2
=8 1/4
=2 Kg m^2
is this correct please tell me
Could you explain what this equation means:

(m1+m2)R=m1r1+m2r2
 
Pablo said:
the center of mass of a system

Pablo said:
moments of inertia of the system about the middle (0.4m)
Is that the centre of mass?
 
Pablo said:
Could you explain what this equation means:

(m1+m2)R=m1r1+m2r2
Is my answer correct?
Learn this equation which i have given
(m1+m2)R=m1r1+m2r2
where m1 and m2 are the given masses
r1 and r2 are their respective positions
R is the position of center of mass
 
The first move is to establish the location of the center of mass. It is the balance point where the torques due to the different weights are equal and opposite. Then the moment of inertia can be calculated as the sum of the m r^2 terms.
 
Dr Dr news said:
The first move is to establish the location of the center of mass. It is the balance point where the torques due to the different weights are equal and opposite.
Are torques and weights needed to find the center of mass of this and other systems?
 
Another way to find the center of mass is to suspend the body and a plumb bob from the same suspension point and repeat using a different point of suspension. Where the two plumb lines cross is the location of the c.m.
 
Dr Dr news said:
Another way to find the center of mass is to suspend the body and a plumb bob from the same suspension point and repeat using a different point of suspension. Where the two plumb lines cross is the location of the c.m.
Isn't there a mathematical way to find the CM using algebra?
 
  • #10
Certainly. If you Google center of mass you will find several equations.
 
  • #11
Dr Dr news said:
Certainly. If you Google center of mass you will find several equations.
I will keep that under advisement. Thanks.
 

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